SOLUTION: the sum three consecutive terms of geometric progression is 26 and the product of them is 216. find three numbers.

Question 881307: the sum three consecutive terms of geometric progression is 26 and the product of them is 216. find three numbers.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
the sum three consecutive terms of geometric progression is 26 and the product of them is 216. find three numbers.
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Equations:
a + ar + ar^2 = 26
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a*ar*ar^2 = (ar)^3 = 216
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ar = cbrt(216) = 6
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Substitute for ar to get:
a + 6 + 6r = 26
a + 6r = 20
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r = 6/a
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a + 36/a = 20
a^2 - 20a + 36 = 0
(a-2)(a-18) = 0
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If a = 2, r = 3
If a = 18, r = 1/3
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Cheers,
Stan H.
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